Show that 15^n can't end with 0 2 4 6 8 for any natural no. n
Answers
Answer:
The prime factorization of 15 doesn't have a 2 and 5 as its factor. So, its factorization will never end in 10 as a number ending in 10 must have a factors as 5 and 2. So, 15n will never end in zero as 15 doesn't has 2 as a factor.
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Question - Show that 15^n can't end with 0 2 4 6 8 for any natural no. n
Answer -
15=3*5
If 15^n is divisible by 10 then it can end with digit zero.
If it is divisible by 10, it has to be divisible by 5 and 2 both.
The prime factorization of 15 is 3×5.
15^n=(3×5)^n
By observation, (3×5) ^n is divisible by 5 but not by 2.
Hence, 15 ^n is not divisible by 10.
Hence, 15 ^n does not end with digit 0 for any natural number n.
Similarly do the same for the other
Hope it helped you
Hope it helped you